x^2+4x-8.25=0

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Solution for x^2+4x-8.25=0 equation: 


Simplifying
x2 + 4x + -8.25 = 0

Reorder the terms:
-8.25 + 4x + x2 = 0

Solving
-8.25 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8.25' to each side of the equation.
-8.25 + 4x + 8.25 + x2 = 0 + 8.25

Reorder the terms:
-8.25 + 8.25 + 4x + x2 = 0 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + 4x + x2 = 0 + 8.25
4x + x2 = 0 + 8.25

Combine like terms: 0 + 8.25 = 8.25
4x + x2 = 8.25

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 8.25 + 4

Reorder the terms:
4 + 4x + x2 = 8.25 + 4

Combine like terms: 8.25 + 4 = 12.25
4 + 4x + x2 = 12.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + 2) equal to 3.5 and -3.5.


Subproblem 1
x + 2 = 3.5

Simplifying
x + 2 = 3.5

Reorder the terms:
2 + x = 3.5

Solving
2 + x = 3.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 3.5 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.5 + -2
x = 3.5 + -2

Combine like terms: 3.5 + -2 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + 2 = -3.5

Simplifying
x + 2 = -3.5

Reorder the terms:
2 + x = -3.5

Solving
2 + x = -3.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = -3.5 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.5 + -2
x = -3.5 + -2

Combine like terms: -3.5 + -2 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -5.5}

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